While I largely agree with what CD says here, this line:
"They would have to believe that the only sure way to get to Heaven is to die killing other human beings in the name of their deity."
Is actually not accurate. Martyrs go to heaven-- but the definition of martyr is loose. It can include those who live the "correct" life of Islam-- presumably, however, that would include acquiesence to it's barbarity-- or it's outright support.
I believe he used the words "only SURE way" advisedly.
But when they tie Jihad and Martyr together...I think that is what CD is refering to.